B.A. Malomed and D.E Pelinovsky

Persistence of the Thomas-Fermi approximation for ground states of the Gros-Pitaevskii equation supported by the nonlinear confinement

Applied Mathematics Letters 40, 45-48 (2015)

We justify the Thomas-Fermi approximation for the stationary Gross-Pitaevskii equation with the repulsive nonlinear confinement, which was recently introduced in physics literature. The method is based on the resolvent estimates and the fixed-point iterations. The results cover the case of the algebraically growing nonlinear confinement.

Gross-Pitaevskii equation, nonlinear confinement, ground states, resolvent estimates, fixed-point iterations.